Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Stochastic Hamiltonian for Non-Critical String Field Theories from Double-Scaled Matrix Models

We present detailed discussions on the stochastic Hamiltonians for non-critical string field theories on the basis of matrix models. Beginning from the simplest $c=0$ case, we derive the explicit forms of the Hamiltonians for the higher critical case $k=3$ (which corresponds to $c=-22/5$) and for the case $c=1/2$, directly from the double-scaled matrix models. In particular, for the two-matrix case, we do not put any restrictions on the spin configurations of the string fields. The properties of the resulting infinite algebras of Schwinger-Dyson operators associated with the Hamiltonians and the derivation of the Virasoro and $W_3$ algebras therefrom are also investigated. Our results suggest certain universal structure of the stochastic Hamiltonians, which might be useful for an attempt towards a background independent string field theory.Comment: 70 pages, LaTeX, typographical errors are corrected, to be published in Phys. Rev.

Editorial: hypotheses about protein folding - the proteomic code and wonderfolds

Theoretical biology journals can contribute in many ways to the progress of knowledge. They are particularly well-placed to encourage dialogue and debate about hypotheses addressing problematical areas of research. An online journal provides an especially useful forum for such debate because of the option of posting comments within days of the publication of a contentious article

Age trajectories of glycaemic traits in non-diabetic South Asian and white individuals: the Whitehall II cohort study.

South Asian individuals have an increased prevalence of type 2 diabetes, but little is known about the development of glycaemic traits in this ethnic group. We compared age-related changes in glycaemic traits between non-diabetic South Asian and white participants

Exact Renormalization Group and Loop Equation

We propose a gauge invariant formulation of the exact renormalization group equation for nonsupersymmetric pure U(N) Yang-Mills theory, based on the construction by Tim Morris. In fact we show that our renormalization group equation amounts to a regularized version of the loop equation, thereby providing a direct relation between the exact renormalization group and the Schwinger-Dyson equations. We also discuss a possible implication of our formulation to the holographic correspondence of the bulk gravity and the boundary gauge theory.Comment: 13 pages, Latex, References added. An error in eq. (6) fixed and a few corrrections accordingly. Results unchange